PSI - Issue 23

Petr Kubík et al. / Procedia Structural Integrity 23 (2019) 15–20 Petr Kubík et al. / Structural Integrity Procedia 00 (2019) 000 – 000

18 4

where  , 0  and a are material constants and  is the normalized Lode parameter, which reads

J

27

2

1   

3

(8)

J

4

3

2

Calibrated material constants are summarized in Tab. 1. These were obtained so that the computational force response matched the experimental one for the flat grooved specimen, where the plane strain is in the specimen’s center. It is in the plane parallel with width. The plane stress is in the same point as well, but through the thickness. The flow curve (Fig. 2) was piece-wise linear. It was estimated on the basis of classical formulae until the ultimate tensile strength. The extrapolation beyond the ultimate tensile strength was realized by the trial and error method so that the computational force response matched the experimental one for dog-bone specimen, where the von Mises and Kroon – Faleskog models of plasticity are identical (due to the uniaxial tension, see Fig. 2). The flow curve was extrapolated to large plastic strains as it is needed, when the simulations run until the moment of fracture (see further). The associated flow rule was used for both yield criteria.

Table 1. Material constants for Kroon – Faleskog yield criterion       0     a  0.123 0.18 4

Fig. 2. The flow curve (left) and initial yield loci in the deviatoric plane (right).

4. Simulations

Numerical simulations were performed within the software package of Abaqus/Explicit. The material model was implemented using the user subroutine Vectorized User MATerial. The 8-node linear brick elements C3D8R were used for geometry discretization. Elements with reduced integration and hourglass control had characteristic size of 0.075 mm in the whole gauge length. The rest of specimens were discretized by elements with the size of 0.2 mm. All the three planes of symmetry were used in all simulations in order to save some computational time. The correctness of Kroon – Faleskog plasticity model implementation was validated towards commercial code of LS-DYNA R8.0.